Evolution equations for continuous-scale morphological filtering
- 1 January 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 42 (12) , 3377-3386
- https://doi.org/10.1109/78.340774
Abstract
Multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks. Morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges. The authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings. These equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals. The nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of a nonlinear function of certain partial differential operatorsKeywords
This publication has 25 references indexed in Scilit:
- Scale-space filtering: A new approach to multi-scale descriptionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Recursive and iterative estimation algorithms for multiresolution stochastic processesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. IISIAM Journal on Numerical Analysis, 1992
- Reconstructions from zero crossings in scale spaceIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Pattern spectrum and multiscale shape representationIEEE Transactions on Pattern Analysis and Machine Intelligence, 1989
- Comments on "The analog median filter" by J.P. Fitch et alIEEE Transactions on Circuits and Systems, 1989
- Subband coding of imagesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1986
- Scaling Theorems for Zero CrossingsIEEE Transactions on Pattern Analysis and Machine Intelligence, 1986
- The structure of imagesBiological Cybernetics, 1984
- Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock WavesPublished by Society for Industrial & Applied Mathematics (SIAM) ,1973